Answer
See below.
Work Step by Step
Let $a,b$ be any integer,
suppose $c=gcd(a,b)$, we can write $a=mc, b=nc$ where $m,n$ are integers without common factors greater than 1.
We have $lcm(a,b)=lcm(mc,nc)=lcm(m,n)\times c=(mn)c$.
Thus we have $c|lcm(a, b)$ and we can reach the conclusion that $gcd(a,b)|lcm(a,b)$
